Question

if n coins are tossed, the probability of x heads is the fraction whose numerator is entry number x of row number n in pascals triangle, and whose denominator is the sum of the entries in row number n. the topmost row of the triangle is
ow number 0\ and the left - most entry of each row is \entry number 0.\ use the pattern in pascals triangle to find the probability of getting 3 heads when seven fair coins are tossed. the probability of getting 3 heads when seven fair coins are tossed is (type an integer or a simplified fraction.)

Explanation:

Step1: Identify row and entry

When 7 coins are tossed, we look at row number 7 in Pascal's triangle. We want the entry for 3 heads, so we find the 4th entry (since we start counting from 0) in row 7. In row 7 of Pascal's triangle: 1, 7, 21, 35, 35, 21, 7, 1, the 4th entry is 35.

Step2: Find row sum

The sum of the entries in row 7 of Pascal's triangle is 128 (as shown in the row - sum column).

Step3: Calculate probability

The probability of getting 3 heads when 7 coins are tossed is the ratio of the entry for 3 heads to the sum of the row. So the probability is $\frac{35}{128}$.

Answer:

$\frac{35}{128}$